Magazines with advertisements do not qualify for Media mail...
4.0 Content Standards for Media Mail
4.1 Qualified Items
Only these items may be mailed at the Media Mail prices:
Books, including books issued to supplement other books, of at least eight printed pages, consisting wholly of reading matter or scholarly bibliography, or reading matter with incidental blank spaces for notations and containing no advertising matter other than incidental announcements of books. Advertising includes paid advertising and the publishers‘ own advertising in display, classified, or editorial style.